Question

In 1908, W. S. Gosset published the article "The Probable Error of a Mean" (Biometrika, Vol. 6, pp. 1-25). In this pioneering paper, written under the pseudonym "Student," Gosset introduced what later became known as Student's t-distribution.
Gosset used the following data set, which gives the additional sleep in hours obtained by a sample of 10 patients using laevohysocyamine hydrobromide.

a. Obtain and interpret a 95% confidence interval for the additional sleep that would be obtained on average for all people using laevohysocyamine hydrobromide. (x = 2.33 hr; s = 2.002 hr.)
b. Was the drug effective in increasing sleep? Explain your answer.